derivative f(x)=sqrt(x)-1/x

Lösung

ableitung von

f (x) = x - \frac{1}{x}

\frac{x ^{\frac{3}{2}} + 2}{2 x ^{\frac{3}{2}} x}

Schritte zur Lösung

\frac{d}{d x} (x - \frac{1}{x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x) - \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= \frac{1}{2 x} - (- \frac{1}{x ^{2}})

Vereinfache

\frac{1}{2 x} - (- \frac{1}{x ^{2}}) : \frac{x ^{\frac{3}{2}} + 2}{2 x ^{\frac{3}{2}} x}

= \frac{x ^{\frac{3}{2}} + 2}{2 x ^{\frac{3}{2}} x}

\frac{d}{d x} (\frac{- 1}{( x - 2 ) ^{2}})

x \to - \infty lim (e^{x} + e^{- x})

\int 16 - 8 x^{2} + x^{4} d x

\int a x^{2} d x

f (x) = \frac{tan ( x ) - 1}{sec ( x )}